>< The Impact of Long-term Memory Effects on Diode Power Probes Hugo Gomes l , 2 , Alejandro R. Testera 3 , Nuno Borges Carvalho I , Monica F. Barciela 3 , Kate A. Remley 4 I - Instituto de Telecomunicar5es - Universidade de Aveiro - Portugal 2 - Instituto Politecnico de Leiria - Portugal, 3 - Universidad de Vigo, Spain 4 - NIST R Fields Group, CO, USA: Partial work of the U. S. goverment, not subject to copyright in the United States Abstract-This paper presents an analysis of long term-memory efects on power measurements with diode power probes. We show that a power probe calibrated with a single-tone sinusoidal excitaton can provide erroneous values when used with modulated signals. This fact is ascribed to the low-frequency response imposed by the power probe baseband circuit. This hypothesis is frst theoretically demonstrated by use of a Volterra series, and then validated by simulations and measurements using a diode power probe. Inde Term-Diode Power Probe, Long-term Memory Efects, Nonlinear Devices, Power Measurement. r. INTRODUCTION D IODE power probes have been used for many years as high-speed power probes, and the results have been quite satisfactory when the power being measured is the power of a simple signal such as a sinusoid [1-3]. The nonlinearity of the diode in these probes rectifes an R signal, providing a representation of the DC power in the signal. However, the nonlinear response of the power probe may depend on the bandwidth of the R input signal, which can be an issue due to increased signal bandwidth of state-of-the-art wireless systems. This behavior can be ascribed to the dynamic interaction of the baseband impedance response and the low fequency voltage and current excited when a nonlinear device under test is excited by any modulated excitation [4]. If not corrected, these dynamic effects may impact the reliability of the measurements. Commercially available microwave power sensors have been designed to work in a 50 Q environment, eliminating impedance mismatches. However, simple diode power detector circuits are used in, for example, cell phone applications, to monitor the received power fom the base station. For these circuits, the baseband embedding impedance can play a key role. In this paper, we will study and analyze the impact of dynamic long-term memory effects on measurements made with diode power probes. This analysis will be done by comparing single-tone and two-tone excitations. The DC voltage corresponding to the detected power will be studied to explain the changes caused by dynamic efects. Long-term memory effects in power amplifers have been studied for many years. They are normally attributed to the low-fequency behavior of the amplifer, due mainly to the bias networks. Both input and output bias matching networks may cause these effects [5]. The fequency response of these networks imposes a change in the nonlinear behavior of the device, mainly introducing asymmetries in the upper and lower third-order intermodulation distortion products as a fnction of the bandwidth of interest. In envelope detectors, this low-fequency interaction is intuitively expected. This is because, for this case, the 978-1-4244-7732-6/101$26.00 ©2010 IEEE 596 objective is to down-convert the signal fom R to the baseband. The impact of nonlinear distortion created by the change of operation to diode power probes is not so obvious. Because we are searching for the DC voltage created by the rectifcation of the diode, we may not expect that the effects of nonlinear distortion in the kilohertz or megahertz range would affect this DC value [1-3]. However, the nonlinear junction capacitance of the diode means that the superposition theorem is not valid anymore. As a result, the output of the diode is diferent for single or multiple tones. In addition, while the use of a single sinusoid does not create any baseband spurious signals, in a multitone arangement, the baseband spurious signals have a bandwidth equivalent to the R bandwidth. These facts have motivated the authors to consider that baseband impedance terminations can affect the accuracy of the DC voltage measured by the probe. In the present work, we will study the impact of these terinations, frst for a single sinusoid and then for a multitone signal. We also will develop methods to predict the effect of the baseband impedance on the measured DC values. We will start frst by presenting this problem with a mathematical approach based on Volterra series analysis. Next in Sections III and IV, an analysis of the impact of the baseband impedance will be carried out by use of both simulations and measurements when the system is excited by a single- and a two-tone signal. Finally, some conclusions will be drawn. II. MATHEMATICAL ANALYSIS In order to understand the basic nonlinear mechanisms of diode power probes, consider the following circuit, in this case a very simple probe, used for demonstration purposes. Fig. 1- Ideal,simplistic diode power probe. A Volterra series-based mathematical approach will be applied to the circuit of Fig.l, considering a minimum number of terms to simplif the understanding of the sought-afer behavior. The diode model [6] is frst approximated by a polynomial series expansion around a quiescent point truncated to order four. Thus the current though the diode is given by: IMS 2010